captan jack harkness

Headcanon: Ten Visited Rose Before Regenerating Because of Jack

So I was pondering how when Jack’s vortex manipulator broke, when he was living in the 20th and 21st centuries he kept an eye on a younger version of Rose who had yet to meet him. This he later tells the Doctor in Utopia. What if that gave the Doctor the idea before he regenerated to see Rose one last time…before she knew him? The Rose who knew him was gone, and he couldn’t have crossed into a point when she already knew him. So without Jack, would he have gone back to New Year’s 2005 to see Rose Tyler one last time?